Cabbage falls prey to the enzymatic browning and oxidation other cut vegetables do, so it's best to leave the heads whole until you need them. However, it's not always that simple. Enzymatic browning, caused by polyphenol oxidase, doesn't occur in an acidic environment, and oxidation can't occur in an oxygen-free environment. So the easiest way to keep cabbage from browning – and keep it crisp by increasing turgor pressure – is with acidulation and submersion.
Quartered or Halved Cabbage
Quartered and halved cabbage heads won't be affected by enzymatic browning or oxidizidation for at least two weeks when you apply citric acid. Cut one or two lemons in half and set them aside, then cut the head of cabbage into quarters or halves. You can leave the core intact on the piece of cabbage you want to store. Rub the cut surface of a lemon half over the cut surface of the cabbage pieces, squeezing occasionally to release some juice. Place the cabbage in a food storage bag and keep it in the vegetable crisper up to two weeks. Don't seal the bag.
Sliced, Shredded or Chopped Cabbage
Cut cabbage has so much surface area that rubbing a lemon over each part of each piece isn't feasible. Squeeze two or three lemons into a bowl and cut the cabbage as desired. Add the cabbage to the bowl, then cover it with cold water. Stir the cabbage in the water so the lemon juice disperses evenly and the acidulated water makes contact with each piece. Cover the bowl with plastic wrap and keep it in the fridge.